Gibbs Free Energy and Reaction Equilibrium Practice Problems (1/2)

Key Concepts in Gibbs Free Energy Calculations

Gibbs Free Energy (∆G)

  • Definition: Gibbs Free Energy is a thermodynamic potential that measures the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure.

  • Formula: ∆G = ∆H - T∆S Where:

    • ∆H = Change in enthalpy

    • T = Temperature in Kelvin

    • ∆S = Change in entropy

Standard Gibbs Free Energy of Formation (AG°f)

  • Definition: The change in Gibbs Free Energy when one mole of a compound is formed from its elements in their standard states.

  • Values Provided:

    • 2 HNO3(aq) : -110.9 kJ/mol

    • NO(g) : 87.6 kJ/mol

    • NO2(g) : 51.3 kJ/mol

    • H2O(l) : -237.1 kJ/mol

Reaction Equilibrium Constant (K)

  • Formula: K = exp(-∆G°/RT) Where:

    • R = Universal gas constant (8.314 J/(mol·K))

    • T = Temperature in Kelvin

Example Calculation for AG

  1. Given Reaction:
    2 Hg(g) + O2(g) → 2 HgO(s)

  2. Provided Data:

    • AG = -180.8 kJ

    • P(Hg) = 0.025 atm

    • P(O2) = 0.037 atm

  3. Utilize Gibb's Energy and Equilibrium:

    • Calculate standard Gibbs free energy for the formation of products and reactants and apply to find K.

Example Calculation for ∆G at Non-standard Conditions

  1. Given Reaction:
    N2(g) + 3 H2(g) ⇌ 2 NH3(g)

  2. Conditions:

    • PN2 = 33.0 atm

    • PH2 = 99.0 atm

    • PNH3 = 2.0 atm

  3. Calculate ∆G at 427°C (700 K):

    • Apply the formula: ∆G = ∆G° + RT ln(Q) Where:

      • Q = (P(NH3)²)/(P(N2) * P(H2)³)

Steps for Solving Problems

  1. Identify Given Data: Note all necessary variables and values given.

  2. Identify Reaction Components: Clearly establish reactants and products.

  3. Choose the Correct Formula: Based on the problem situation (Equilibrium, Standard, or Non-standard conditions).

  4. Perform Calculations: Execute the mathematical operations step by step, ensuring units are consistent.

  5. Interpret Results: Understanding the implications of the value of ∆G (negative, positive, or zero) as it relates to spontaneity and equilibrium.